## Abstract

With phase-shifting joint transform correlation (PSJTC) one
uses multiple phase shifts to recover the phase difference between
Fourier transforms of the input and the reference. In PSJTC systems
the resulting phase-only function is used instead of the joint
transform power spectrum (JTPS). Provided it can be recorded
linearly, the JTPS reduces to a modulated sinusoidal fringe, especially
when the target image matches the reference image. In practice, the
JTPS has a wide dynamic range, and a CCD camera has a nonlinear
response. Correspondingly, the recorded JTPS turns out to be
different from a perfect sinusoidal fringe. Here we study the
dynamic range effects of realizing PSJTC with the phase-iterative
algorithm.

© 1999 Optical Society of America

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### Equations (6)

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(1)
$${J}_{n}\left(u,v\right)=|F\left(u,v\right){|}^{2}+|R\left(u,v\right){|}^{2}+2|F\left(u,v\right)\Vert R\left(u,v\right)|\times cos\left[2\mathit{bu}+{\mathrm{\varphi}}_{F}\left(u,v\right)-{\mathrm{\varphi}}_{R}\left(u,v\right)+{\mathrm{\delta}}_{n}\right],$$
(2)
$${\mathrm{\varphi}}_{\mathrm{JTPS}}={\mathrm{\varphi}}_{F}\left(u,v\right)-{\mathrm{\varphi}}_{R}\left(u,v\right)={tan}^{-1}\left[{3}^{1/2}\left({J}_{2}-{J}_{1}\right)/\left(2{J}_{0}-{J}_{1}-{J}_{2}\right)\right]-2\mathit{bu}.$$
(3)
$$\mathit{PJ}=exp\left(j{\mathrm{\varphi}}_{\mathrm{JTPS}}\right)=exp\left\{{tan}^{-1}\left[{3}^{1/2}\left({J}_{2}-{J}_{1}\right)/\left(2{J}_{0}-{J}_{1}-{J}_{2}\right)\right]-2\mathit{bu}\right\}$$
(4)
$$I\left(u,v\right)=1+cos\left[{\mathrm{\varphi}}_{\mathrm{JTPS}}+\left(2\mathrm{\pi}/N\right)i\right],$$
(5)
$${J}_{\mathit{sn}}\left(u,v\right)=\left\{\begin{array}{cc}1,& {J}_{n}\left(u,v\right)R\\ {J}_{n}\left(u,v\right)/R,& \mathrm{otherwise}\end{array}\right.,$$
(6)
$$\mathrm{\Delta}=\left({P}_{2}-{P}_{2}\right)/{P}_{1},$$